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Matrix CompletionWith Noise Emmanuel J. CandèsYaniv Plan2010 год

Matrix Completion With Noise
статья из журнала

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Аннотация: On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries. It comes up in many areas of science and engineering, including collaborative filtering, machine learning, control, remote sensing, and computer vision, to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown matrix of low rank from just about log noisy samples with an error that is proportional to the noise level. We present numerical results that complement our quantitative analysis and show that, in practice, nuclear-norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout.
Год издания: 2010
Авторы: Emmanuel J. Candès, Yaniv Plan
Издательство: Institute of Electrical and Electronics Engineers
Источник: Proceedings of the IEEE
Ключевые слова: Sparse and Compressive Sensing Techniques, Blind Source Separation Techniques, Image and Signal Denoising Methods
Другие ссылки: Proceedings of the IEEE (HTML)
CaltechAUTHORS (California Institute of Technology) (PDF)
CaltechAUTHORS (California Institute of Technology) (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)